A) \[M={{m}_{\operatorname{proton}}}+{{m}_{\operatorname{electron}}}\]
B) \[M={{m}_{\operatorname{proton}}}+{{m}_{\operatorname{electron}}}-\frac{B}{{{c}^{2}}}\] \[(B=13.6ev)\]
C) M is not related to the mass of the hydrogen atom.
D) \[M={{m}_{\operatorname{proton}}}+{{m}_{\operatorname{electron}}}-\frac{|V|}{{{c}^{2}}}(|V|=\]magnitude of the potential energy of electron in the H-atom).
Correct Answer: B
Solution :
Option (b) is correct. Explanation: During formation of H-atom, some mass of nucleons convert into energy by the equation \[E=m{{c}^{2}}\] This energy is used to bind the nucleons along with nucleus. So mass of atom becomes slightly less than sum of actual masses of nucleons and electrons. Actual mass of H-atom = \[{{M}_{p}}={{M}_{e}}-\frac{\operatorname{B}.E.}{{{c}^{2}}}\left( \frac{\operatorname{B}}{{{c}^{2}}}=\operatorname{Binding} energy \right)\] So, the binding energy of H atoms is 13.6 eV per atom.
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